List of top Mathematics Questions

The equation of parabola whose focus is (6, 0) and directrix is x = –6 is

A diet is to contain $30$ units of vitamin $A$, $40$ units of vitamin $B$ and $20$ units of vitamin $C$. Three types of foods $F_{1}$, $F_{2}$ and $F_{3}$ are available. 1 unit of food $F_{1}$ contains $3$ units of vitamin $A$, $2$ units of vitamin $B$, $1 $ unit of vitamin $C$. $1$ unit of food $F_{2}$ contains $1$ unit of vitamin $A$, $2$ units of vitamin $B$ and $1$ unit of vitamin $C$. $1$ unit of food $F_{3}$ contains $5$ units of vitamin $A$, $3$ units of vitamin $B$ and $2$ units of vitamin $C$. Represent the above situation algebraically and find the diet contains each types of food by using matrix method.

If solution of differential equation xdy - ydx = xy(xdy - ydx) and y(1) = 1 is α|y| = |x|e^{(xy - β)} then (α + β) is equal to

The value of \( \left| \int_{0}^{\infty} \left( 3 + i \right) \left( \bar{z} \right)^2 \, dz \right| \), along the line \( 3y = x \), where \( z = x + jy \), is ............

The vectors of magnitude $a, 2a, 3a $ meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

Multiply and reduce to lowest form (if possible) :
(i) \(\frac{2}{3}\) × 2 \(\frac{2}{3}\)
(ii) \(\frac{2}{7}\) × \(\frac{7}{9}\)
(iii) \(\frac{3}{8}\) × \(\frac{6}{4}\)
(iv) \(\frac{9}{4}\) × \(\frac{3}{5}\)
(v) \(\frac{1}{3}\)× \(\frac{15}{8}\)
(vi) \(\frac{11}{2}\) × \(\frac{3}{10}\)
(vii) \(\frac{4}{5}\) × \(\frac{12}{7}\)

Let $A=\{1,2,3,5,8,9\}$ Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to______

Find the product:
(i)\(\frac{9}{2}\)×(-\(\frac{7}{4}\))
(ii) \(\frac{3}{10}\)×(-9)
(iii) -\(\frac{6}{5}\)×\(\frac{9}{11}\)
(iv) \(\frac{3}{7}\)×(-\(\frac{2}{5}\))
(v) \(\frac{3}{11}\)×\(\frac{2}{5}\)
(vi) \(\frac{3}{-5}\) ×\(\frac{-5}{3}\)

Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h.
\includegraphics[width=\linewidth]{latex.png} The relation between fuel consumption \( F \) (liters per 100 km) and speed \( V \) (km/h) under some constraints is given as: \[ F = \frac{V^2}{500} - \frac{V}{4} + 14. \] On the basis of the above information, answer the following questions: [(i)] Find \( F \), when \( V = 40 \, \text{km/h} \). [(ii)] Find \( \frac{dF}{dV} \). [(iii)] (a) Find the speed \( V \) for which fuel consumption \( F \) is minimum.
\hspace*{0.8cm} OR
(b) Find the quantity of fuel required to travel \( 600 \, \text{km} \) at the speed \( V \) at which \( \frac{dF}{dV} = -0.01 \).

Draw, wherever possible, a rough sketch of 

1.  a triangle with both line and rotational symmetries of order more than 1. 
2.  a triangle with only line symmetry and no rotational symmetry of order more than 1. 
3.  a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry. 
4.  a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point is

Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

Multiply and reduce to the lowest form and convert into a mixed fraction:
(i) 7 × \(\frac{3}{5}\)
(ii) 4 × \(\frac{1}{3}\)
(iii) 2 × \(\frac{6}{7}\)
(iv) 5 ×\(\frac{2}{9}\)
(v) \(\frac{2}{3}\)× 4
(vi) \(\frac{5}{2}\) × 6
(vii) 11 × \(\frac{4}{7}\)
(viii) 20 × \(\frac{4}{5}\)
(ix) 13 × \(\frac{1}{3}\)
(x) 15 × \(\frac{3}{5}\)

Express the following numbers in standard form:
(i) 5,00,00,000 (ii) 70,00,000 (iii) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78

If a, b, c are in increasing A.P. and a + 1, b, c + 3 are in G.P. If A.M. of a, b, c is 8. Find cube of G.M. of a, b, c.

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

If $^{n}C_{r-1}=28$, $^{n}C_{r}=56$ and $^{n}C_{r+1}=70$, then the value of $r$ is equal to

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

Add the following. l² + m², m² + n², n² + l², 2lm + 2mn + 2nl